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In this paper, we apply information theory measures and Markov processes in order to analyse the inequality in the distribution of the financial risk in a pool of countries. The considered financial variables are sovereign credit ratings and interest rates of sovereign government bonds of European countries. This paper extends the methodology proposed in our previous work, by allowing the possibility to consider a continuous time process for the credit rating evolution so that complete observations of rating histories and credit spreads can be considered in the analysis. Obtained results suggest that the continuous time model fits real data better than the discrete one and confirm the existence of a different risk perception among the three main rating agencies: Fitch, Moody's and Standard & Poor's. The application of the model has been performed by a software we developed, the full code is available on-line allowing the replication of all results.

In this paper, we propose a methodology based on piecewise homogeneous Markov chain for credit ratings and a multivariate model of the credit spreads to evaluate the financial risk in European Union (EU). Two main aspects are considered: how the financial risk is distributed among the European countries and how large is the value of the total risk. The first aspect is evaluated by means of the expected value of a dynamic entropy measure. The second one is solved by computing the evolution of the total credit spread over time. Moreover, the covariance between countries' total spread allows understand any contagions in the EU. The methodology is applied to real data of 24 European countries for the three major rating agencies: Moody's, Standard & Poor's and Fitch. Obtained results suggest that both the financial risk inequality and the value of the total risk increase over time at a different rate depending on the rating agency and that the dependence structure is characterized by a strong correlation between most of European countries.

In the present work, we investigate the sensitivity of the dynamic Theil index computed under a Markov reward model with respect to structured perturbations affecting the underlying Markov process. The model is applied to the sovereign credit spread evolution as a proxy for financial risk, which are driven by the sovereign credit rating dynamic. The introduction of such perturbations allows to evaluate the sensitivity of the inequality of the financial risk in a given group of financial entities with respect to the uncertainty in the rating dynamics. To this end we perform a simulation based sensitivity analysis. The methodology is applied to real data concerning sovereign credit ratings and long-term interest rates on government bonds of 24 European countries. Obtained results suggest different sensitivity of the inequality measure to the 12 scenarios built supposing different ways the perturbations could affect the rating process.

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